The 95% confidence interval for B₁ is the interval: A. (B₁ - 1.645SE (1), ₁ + 1.645SE (B1)). B. (ẞ1-1.96SE (B1), ß₁ + 1.96SE (ß₁)) · ○ C. (₁ - 1.96, ³₁ + 1.96). - D. (³₁ − 1.96SE (³₁), ³₁ + 1.96SE (γ₁)). 8 Consider the regression model Y₁ = BX; +u; Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ Show that ẞ is a linear function of Y₁, Y2,..., Y. 1 +Yn) | (X1, X2,..., Xn) = Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2, Xn) = 2. E(B|×₁, X2,..., Xn) = E 1 3 II where Y and X are the sample means of Y; and X;, respectively. ☑' = B

A recent survey showed that in a sample of 180 high school teachers, 36 were single. In a sample of 100 elementary school teachers, 15 were single. Is the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single? Use α = 0.01.

The following data represent the number of touchdown passes thrown by a particular quarterback during his first 18 seasons. Verify that Chebyshev's Theorem holds true by determining the percent of observations that fall within tone, two, a three standard deviations from the mean. " 16 17 34 37 37 30 35 21 19 31 30 33 28 19 16 29 24 What is the mean of the data set? x=(Type an integer or decimal rounded to two decimal places as needed.) What is the standard deviation of the data set? s= (Round to two decimal places as needed.) Calculate the interval xts. x+s = OD (Round to two decimal places as needed. Type your answer in interval notation.) What percentage of the data values fall within the interval xts? The percentage of data values that fall within the interval is % (Round to the nearest percent as needed.) Calculate the interval x+ 2s. x+2s = (D (Round to two decimal places as needed. Type your answer interval notation.) What percentage of the data values fall within the interval…

A physician wants to see if there was a difference in the average smokers' daily cigarette consumption after wearing a nicotine patch. The physician set up a study to track daily smoking consumption. In the study, the patients were given a placebo patch that did not contain nicotine for 4 weeks, then a nicotine patch for the following 4 weeks. Test to see if there was a difference in the average smoker's daily cigarette consumption using α = 0.01. The hypotheses are: H0 : μD = 0 H1 : μD ≠ 0 t-Test: Paired Two Sample for Means         Placebo Nicotine Mean 18.75 12.3125 Variance 66.599 34.6667 Observations 16 16 Pearson Correlation 0.6105   Hypothesized Mean Difference 0   df 15   t Stat 3.5481   P(T<=t) one-tail 0.0126   t Critical one-tail 2.6025   P(T<=t) two-tail 0.0252   t Critical two-tail 2.9467     What is the correct p-value?   Question 1 options:…

Examine (A), (B) and (C) and find the relationship between 40 % of 60 30% od 80 20% of 240 a. A=CB b. A+B=C c. 2A=B d. A+C=B e. None   examine (A), (B), and (C), find the correct relationship between them. (A): 136/117+7 (B): 9133 X27) /171 (C): (237/3)- (33-17) C=4B +A C=A+B A=4B 4B=C+A None

Let u = (1, 0, - 5) and Compute the following: ú. v = v. u= ||ū||² = - 10(u. v) = ( - 10u) v = . u. (-10%) (ú. v) v = = = (3, 7, 6).

A survey was conducted among 73 patients admitted to a hospital cardiac unit during a two-week period. The data of the survey are shown below. Let B = the set of patients with high blood pressure. Let C= the set of patients with high cholesterol levels. Let S = the set of patients who smoke cigarettes. Answer parts (a)-(d) below. n(B) = 33 n(C) = 30 n(S) = 27 n(BNS) = 8 n(B n C) = 10 n(B n cns) = 3 n[(BNC) U (BNS) U (CNS)] = 20 C... (a) Find the number of these patients that had either high blood pressure or high cholesterol levels, but not both. The number of cities that had high blood pressure or high cholesterol levels, but not both, is. (b) Find the number of these patients that had fewer than two of the indications listed. The number of patients that had fewer than two of the indications listed is. (c) Find the number of these patients that were smokers but had neither high blood pressure nor high cholesterol levels. The number of patients that were smokers but had neither high…

In a survey of 1150 adult males, 805 said they use the Internet. In a survey of 1050 females, 746 said they use the Internet. At α= 0.05, can you reject the claim that the proportion of Internet users are the same for both groups?

The values for P(A₁B) and P(A₂B) were found to be 0.20 and 0.02, respectively. Use these values to calculate P(A₁ | B) to four decimal places. P(A₁ | B) = P(A, B) P(A₁B) + P(A₂ MB) 0.20 0.20+ 0.02 = 0.22 X